The Constitution does not specify the size of the Supreme Court, which actually changed multiple times throughout the 1800s.
Why do you specifically call out Democrats here? The most recent court size increase was during the presidency of Grant, a Republican.
Anyway, regarding the original topic of the National Popular Vote compact, the Constitution does not specify how each state chooses its electors in the Electoral Collage. Initially, most state legislatures chose their electors without any popular vote at all!
Eventually all states switched to a popular vote system, individually, but this took several decades to occur. That initial switch seems more substantial than what is proposed in the National Popular Vote compact, so why are you confidently proclaiming that it would result in a civil war?